Quadratic Equations in Three Variables over Gaussian Integers
Felix Sidokhine
TL;DR
This paper introduces an algebraic approach to analyze quadratic Diophantine equations in three variables over Gaussian integers, expanding understanding of solutions in this complex integer domain.
Contribution
It presents a novel algebraic method specifically designed for solving quadratic equations over Gaussian integers, which was not previously available.
Findings
New algebraic framework for quadratic equations over Gaussian integers
Characterization of solutions in the Gaussian integer domain
Potential applications to number theory problems
Abstract
We develop an algebraic method of studying of Diophantine quadratic equations in three variables over the ring of Gaussian integers.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · advanced mathematical theories